Summary

Bob Blitzer's books are highly acclaimed for their well-conceived, relevant applications and meticulously annotated examples. This highly anticipated revision achieves the difficult balance between coverage and motivation, while helping readers develop strong problem-solving skills. This book provides readers with the skill building and practice that is so crucial as well as the applications and technology necessary to foster an appreciation of the myriad uses of mathematics. This book covers a wide range of topics including set theory, logic, number theory, algebra, consumer mathematics and financial management, geometry, measurement, probability theory and statistics. For anyone interested in refreshing his/her fundamental math skills.

Author Biography

Bob Blitzer has taught a variety of mathematics courses at Miami-Dade Community College for nearly 30 years

Table of Contents

About the Author

viii

Preface

ix

To the Student

xi

Acknowledgments

xiii

Resources

xx

Applications Index

xxi

Problem Solving and Critical Thinking

3

(38)

Inductive and Deductive Reasoning

4

(9)

Estimation and Graphs

13

(11)

Problem Solving

24

(17)

Summary

36

(1)

Review Exercises

36

(2)

Chapter 1 Test

38

(3)

Set Theory

41

(50)

Basic Set Concepts

42

(11)

Venn Diagrams and Subsets

53

(11)

Venn Diagrams and Set Operations

64

(7)

Set Operations and Venn Diagrams with Three Sets

71

(8)

Surveys and Cardinal Numbers

79

(12)

Summary

87

(1)

Review Exercises

88

(2)

Chapter 2 Test

90

(1)

Logic

91

(78)

Statements, Negations, and Quantified Statements

92

(6)

Compound Statements and Connectives

98

(11)

Truth Tables for Negation, Conjunction, and Disjunction

109

(13)

Truth Tables for the Conditional and Biconditional

122

(11)

Equivalent Statements, Conditional Statements, and De Morgan's Laws

133

(11)

Arguments and Truth Tables

144

(11)

Arguments and Euler Diagrams

155

(14)

Summary

164

(1)

Review Exercises

165

(2)

Chapter 3 Test

167

(2)

Number Representation and Calculation

169

(34)

Our Hindu-Arabic System and Early Positional Systems

170

(7)

Number Bases in Positional Systems

177

(7)

Computation in Positional Systems

184

(7)

Looking Back at Early Numeration Systems

191

(12)

Summary

198

(1)

Review Exercises

198

(2)

Chapter 4 Test

200

(3)

Number Theory and the Real Number System

203

(72)

Number Theory: Prime and Composite Numbers

204

(9)

The Integers; Order of Operations

213

(11)

The Rational Numbers

224

(11)

The Irrational Numbers

235

(9)

Real Numbers and Their Properties

244

(6)

Exponents and Scientific Notation

250

(11)

Arithmetic and Geometric Sequences

261

(14)

Summary

269

(2)

Review Exercises

271

(3)

Chapter 5 Test

274

(1)

Algebra: Equations and Inequalities

275

(70)

Algebraic Expressions and Formulas

276

(10)

Solving Linear Equations

286

(12)

Applications of Linear Equations

298

(9)

Ratio, Proportion, and Variation

307

(11)

Solving Linear Inequalities

318

(9)

Solving Quadratic Equations

327

(18)

Summary

339

(1)

Review Exercises

340

(3)

Chapter 6 Test

343

(2)

Algebra: Graphs, Functions, and Linear Systems

345

(74)

Graphing and Functions

346

(11)

Linear Functions and Their Graphs

357

(10)

Quadratic Functions and Their Graphs

367

(11)

Exponential Functions

378

(6)

Systems of Linear Equations

384

(14)

Linear Inequalities in Two Variables

398

(8)

Linear Programming

406

(13)

Summary

413

(1)

Review Exercises

414

(3)

Chapter 7 Test

417

(2)

Consumer Mathematics and Financial Management

419

(58)

Percent

420

(10)

Interest

430

(11)

Installment Buying

441

(12)

The Cost of Home Ownership

453

(9)

Investing in Stocks, Bonds, and Mutual Funds

462

(15)

Summary

472

(1)

Review Exercises

473

(2)

Chapter 8 Test

475

(2)

Measurement

477

(28)

Measuring Length; The Metric System

478

(10)

Measuring Area and Volume

488

(8)

Measuring Weight and Temperature

496

(9)

Summary

502

(1)

Review Exercises

503

(1)

Chapter 9 Test

504

(1)

Geometry

505

(74)

Points, Lines, Planes, and Angles

506

(9)

Triangles

515

(11)

Polygons, Quadrilaterals, and Perimeter

526

(6)

Area and Circumference

532

(11)

Volume

543

(9)

Right Triangle Trigonometry

552

(9)

Beyond Euclidian Geometry

561

(18)

Summary

571

(1)

Review Exercises

572

(4)

Chapter 10 Test

576

(3)

Counting Methods and Probability Theory

579

(76)

The Fundamental Counting Principle

578

(8)

Permutations

586

(8)

Combinations

594

(7)

Fundamentals of Probability

601

(10)

Probability with the Fundamental Counting Principle, Permutations, and Combinations